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Standard Form of a Quadratic Function

The standard form of a quadratic function is a quadratic function written in a specific format.

Here, and are real numbers with The term with the highest degree — the quadratic term — is written first. Then, the linear term followed by the constant term are written. The standard form can be used to determine the direction of the parabola, the intercept, the axis of symmetry, and the vertex.

Direction of the Graph Opens upward when
Opens downward when
Axis of Symmetry

Standard Form of a Quadratic Equation

Similar to a quadratic function, a quadratic equation can be written in standard form. This is called the standard form of a quadratic equation.
In this equation, is not equal to The solutions of a quadratic equation written in this form can be found by applying the Quadratic Formula.

Rewriting a Quadratic Function in Standard Form

Both the vertex and the intercept form of a quadratic function can always be written in standard form.

Form Equation How to Rewrite?
Vertex Form Expand distribute and combine like terms.
Intercept Form Multiply and combine like terms.